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# Fourth power of 2^(root(2) is:

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Intern
Joined: 19 May 2014
Posts: 31
Fourth power of 2^(root(2) is: [#permalink]

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Updated on: 22 May 2014, 05:23
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2
00:00

Difficulty:

35% (medium)

Question Stats:

53% (00:46) correct 47% (00:31) wrong based on 175 sessions

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Fourth power of $$2^{\sqrt{2}$$ is:

(A) 4
(B) $$16^{\sqrt{2}$$
(C) 16
(D) 64
(E) 256

Source: Original Question

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Originally posted by JapinderKaur on 22 May 2014, 05:18.
Last edited by Bunuel on 22 May 2014, 05:23, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 47006
Re: Fourth power of 2^(root(2) is: [#permalink]

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22 May 2014, 05:30
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MavenQ wrote:
Fourth power of $$2^{\sqrt{2}$$ is:

(A) 4
(B) $$16^{\sqrt{2}$$
(C) 16
(D) 64
(E) 256

Source: Original Question

$$(a^m)^n=a^{mn}$$

$$a^m^n=a^{(m^n)}$$ and not $$(a^m)^n$$ (if exponentiation is indicated by stacked symbols, the rule is to work from the top down)

Thus, $$(2^{\sqrt{2}})^4=2^{4\sqrt{2}}=16^{\sqrt{2}}$$.

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

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Re: Fourth power of 2^(root(2) is: [#permalink]

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22 May 2014, 21:47

$${a^b}^{c} = a^{(b^c)}$$

$$(a^b)^c = a^{bc}$$

For example:

$${2^3}^{2}= 2^9 = 512$$

$$(2^3)^2 = 2^6 = 64 Or$$

$$(2^3)^2 = 8^2 = 64$$
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Re: Fourth power of 2^(root(2) is: [#permalink]

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29 Sep 2017, 00:07
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Fourth power of 2^(root(2) is:   [#permalink] 29 Sep 2017, 00:07
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